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The Peierls Instability in Metal Nanowires Daniel Urban (Albert-Ludwigs Universität Freiburg, Germany) In collaboration with C.A.Stafford and H.Grabert
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Peierls Instability is a distortion energetically favorable? max energy gain for EFEF
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This model requires: good charge screening almost spherical Fermi-surface NFEM is suitable for s-orbital-metals (alkali metals, gold) Nanoscale Free-Electron Model (NFEM) free electrons + confining potential ions = incompressible homogeneous background nanowire = quantum waveguide open system connected to reservoirs scattering problem
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eigenenergies NFEM: Nanowire = Waveguide transverse wave function (modes, channels) wave function EFEF quantized motion in x-y-plane free motion in z-direction k F,1 k F,n
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Difference from standard Peierls theory: no periodic boundary conditions Peierls Instability at Length L Cylindrical wire + perturbation Pseudo gap, energy gap only for nanowire with finite length L system = nanowire + leads
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Surface Phonons Ions = incompressible fluid Born-Oppenheimer approximation Phonon frequency mode stiffness mode inertia Grand canonical potential:
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Scattering Matrix Formalism density of statesgrand canonical potential
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Grand canonical potential mode stiffness Mode Stiffness Cylindrical nanowire + perturbation L C : critical length
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Dispersion Relation
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CDW Correlations Crossover: L<L C : small fluctuations about cylindrical shape L>L C : CDW with quantum fluctuations, no long-range order
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Finite-size Scaling Scaling of the mode stiffness: Length scale Energy scale critical length Critical point and
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Correlation length ξ n ξ is material dependent & tunable by applying strain singular part of the mode stiffness
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Summary Peierls instability in metal nanowires at L=L C ~ξ Further reading: DFU, Stafford, Grabert, cond-mat/0610787 DFU, Grabert, PRL 91, 256803 Hyperscaling of the singular part of the free energy CDW in metal nanowires should be experimentally observable under strain
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